Post-selection inference for causal effects after causal discovery.

Area of Science:

• Statistics
• Machine Learning
• Causal Inference

Background:

• Constraint-based causal discovery algorithms identify graphical causal models using conditional independence tests.
• These models inform causal effect estimation but face challenges with valid inference post-selection.
• Naive data usage for both model selection and estimation yields invalid confidence intervals.

Purpose of the Study:

• To develop a post-selection inference method for causal discovery that provides asymptotically correct coverage for causal effect parameters.
• To address the issue of invalid confidence intervals arising from using data twice in causal discovery and estimation.
• To ensure inferential claims are valid for population-level effects, not data-dependent quantities.

Main Methods:

• A resampling and screening procedure is proposed, performing causal discovery multiple times with randomized intermediate statistics.
• Causal effect estimates and confidence sets are constructed by uniting individual graph-based results.
• The approach is demonstrated using the PC-algorithm for directed acyclic graphs and multivariate Gaussian distributions.

Main Results:

• The proposed method achieves asymptotically correct coverage for the true causal effect parameter.
• The confidence sets are guaranteed to be valid for a fixed population-level effect.
• The approach is general and modular, applicable to various discovery algorithms and distributional families.

Conclusions:

• The developed post-selection inference technique offers a statistically sound method for causal effect estimation following model selection.
• This approach enhances the reliability of causal inference in the presence of uncertainty about model structure.
• The method's modularity allows for broad applicability across different causal discovery frameworks.